1. The following production function is used to produce wheat, q, from capi- tal, K, and labour, L: q = f(K, L) = a?K/3+ B³L/3 a) Describe the role of a and B in this production function. b) Derive the slope of an isoquant for this production function and in- terpret your result. Draw the isoquant in (K - L) space, labeling where appropriate. The drawing does not need to be exact, but the curvature needs to be approximately correct. Explain why under- standing the curvature is so important. c) Does this production function follow the "Law of Diminishing Marginal Returns"? Show your work and explain your answer.
1. The following production function is used to produce wheat, q, from capi- tal, K, and labour, L: q = f(K, L) = a?K/3+ B³L/3 a) Describe the role of a and B in this production function. b) Derive the slope of an isoquant for this production function and in- terpret your result. Draw the isoquant in (K - L) space, labeling where appropriate. The drawing does not need to be exact, but the curvature needs to be approximately correct. Explain why under- standing the curvature is so important. c) Does this production function follow the "Law of Diminishing Marginal Returns"? Show your work and explain your answer.
Chapter10: Cost Functions
Section: Chapter Questions
Problem 10.9P
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Question
Transcribed Image Text:1. The following production function is used to produce wheat, q, from capi-
tal, K, and labour, L:
q = f(K, L) = «³K/3
+ B³L/3
a) Describe the role of a and B in this production function.
b) Derive the slope of an isoquant for this production function and in-
terpret your result. Draw the isoquant in (K L) space, labeling
where appropriate. The drawing does not need to be exact, but the
curvature needs to be approximately correct. Explain why under-
standing the curvature is so important.
|
c) Does this production function follow the "Law of Diminishing
Marginal Returns"? Show your work and explain your answer.
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